A 25-year-old man was on Monday charged with committing an unlawful act with intent to cause grievous bodily harm, aggravated assault and other gun offences.
It is alleged a group of five people, including the teenage boy, tried to enter the man's house in South Hobart around 1.20am.
It is believed they fled when a shot was fired, police say.
The teenager, who was shot in the back, has undergone surgery and remains in a critical but stable condition in the Royal Hobart Hospital.
"We understand that the victim in this matter has been conveyed to the hospital by associates of his and essentially left there," Tasmania Police Inspector David Gill told reporters.
The shooting could be linked to a road rage incident about two days earlier, but investigations were in the initial stages, Insp Gill said.
An unregistered shotgun was recovered from the scene by police.
Syme Street in South Hobart is near a popular rivulet walking track and backs onto a world heritage listed 19th century workhouse built to "reform" female convicts.
The arrested man is expected to appear in Hobart Magistrates Court on Tuesday.
Police believe there were witnesses to the shooting and have asked anyone with information to come forward.
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